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Chapter 10: Problem 38

A road is inclined at an angle of \(5^{\circ}\). After driving 5000 feet along this road, find the driver's increase in altitude. Round to the nearest foot.

Short Answer

Expert verified
The increase in altitude is calculated to be approximately 436 feet, when rounded to the nearest foot.

Step by step solution

01

Understanding the relationship

In this problem, we are dealing with the vertical increase in altitude. This means, the driver is not climbing the entire 5000 feet upwards vertically, but only a portion of it as the road is inclined. Therefore, this creates a right angled triangle between the flat ground, the road (hypotenuse) and the vertical altitude. We know the length of the hypotenuse (5000 feet) and the angle of inclination (5 degrees). For calculating the increase in altitude, we will use the sine function (sin) because sin of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to that of the hypotenuse.
02

Applying the sine function

The sine function lets us to calculate the altitude increase as follows: Altitude increase = sine (angle) x hypotenuse length. Therefore, the increase in altitude is = \(\sin(5^{\circ}) \times 5000 \) feet.
03

Calculate and round the result

Perform the calculation. The result is in feet. Since the question asks us to round our answer to the nearest foot, make sure to appropriately round off your answer. If the result after the decimal point is five or above, round up to the next whole number. If it is less than five, round down.

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